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  "cells": [
    {
      "metadata": {
        "id": "eQ7K9blSUKTs",
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      "source": [
        "Copyright 2019 Google LLC\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\"); you may not use this file except in compliance with the License. You may obtain a copy of the License at\n",
        "\n",
        "https://www.apache.org/licenses/LICENSE-2.0\n",
        "\n",
        "Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an \"AS IS\" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.\n",
        "\n",
        "# (Attentive) Neural Processes for 1D regression\n",
        "\n",
        "Regression is usually cast as modelling the distribution of output **y** given input **x** via a deterministic function, such as a neural network, taking **x** as input. In this setting, the model is trained on a dataset of input-output pairs, and predictions of the outputs are independent of each other given the inputs. An alternative approach to regression involves using the training data to compute a distribution over functions that map inputs to outputs, and using draws from that distribution to make predictions on test inputs. This approach allows for reasoning about multiple functions consistent with the data, and can capture the co-variability in outputs given inputs. In the Bayesian machine learning literature, non-parametric models such as Gaussian Processes (GPs) are popular choices of this approach.\n",
        "\n",
        "[Neural Processes](https://arxiv.org/abs/1807.01622) (NPs) also approach regression by modelling a distribution over regression functions. Each function models the distribution of the output given an input, conditioning on some observed input-output pairs, which we call the context. Modelling this distribution over functions was made possible by incorporating a latent variable to the [Conditional Neural Process](https://arxiv.org/abs/1807.01613) (CNP). \n",
        "\n",
        "However NPs suffer from underfitting, giving inaccurate predictions at the inputs of the observed data they condition on. Hence [Attentive Neural Processes](https://arxiv.org/abs/1901.05761) (ANPs) were introduced, addressing this issue by incorporating attention into NPs. We share the implementation of ANPs (and NPs, which is a special case of ANP with uniform attention) for a 1D regression task where (A)NPs are trained on random 1D functions."
      ]
    },
    {
      "metadata": {
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      "cell_type": "markdown",
      "source": [
        "## Imports"
      ]
    },
    {
      "metadata": {
        "id": "Ncb7M0FpNfix",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import tensorflow as tf\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import collections"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "ARGYAmEsa5K7",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Data generator\n",
        "Instead of training using observations from a single function (as in classic regression tasks), we would like to train on a dataset that comes from multiple functions with shared characteristics. Hence for training, we use data that comes from a Gaussian Process (GP) with randomly varying kernel parameters.  At each training iteration, we sample a batch of random kernel parameters, and for each parameter setting we sample a curve (a realisation) from the corresponding GP. We select random points on each curve to be the targets and a subset to be the contexts for optimising the training loss. The data generation is almost the same as for the [implementation of CNPs](https://github.com/deepmind/conditional-neural-process/blob/master/conditional_neural_process.ipynb), but with kernel parameters varying randomly at each iteration."
      ]
    },
    {
      "metadata": {
        "id": "Px-atGEfNnWT",
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      "cell_type": "code",
      "source": [
        "# The (A)NP takes as input a `NPRegressionDescription` namedtuple with fields:\n",
        "#   `query`: a tuple containing ((context_x, context_y), target_x)\n",
        "#   `target_y`: a tensor containing the ground truth for the targets to be\n",
        "#     predicted\n",
        "#   `num_total_points`: A vector containing a scalar that describes the total\n",
        "#     number of datapoints used (context + target)\n",
        "#   `num_context_points`: A vector containing a scalar that describes the number\n",
        "#     of datapoints used as context\n",
        "# The GPCurvesReader returns the newly sampled data in this format at each\n",
        "# iteration\n",
        "\n",
        "NPRegressionDescription = collections.namedtuple(\n",
        "    \"NPRegressionDescription\",\n",
        "    (\"query\", \"target_y\", \"num_total_points\", \"num_context_points\"))\n",
        "\n",
        "\n",
        "class GPCurvesReader(object):\n",
        "  \"\"\"Generates curves using a Gaussian Process (GP).\n",
        "\n",
        "  Supports vector inputs (x) and vector outputs (y). Kernel is\n",
        "  mean-squared exponential, using the x-value l2 coordinate distance scaled by\n",
        "  some factor chosen randomly in a range. Outputs are independent gaussian\n",
        "  processes.\n",
        "  \"\"\"\n",
        "\n",
        "  def __init__(self,\n",
        "               batch_size,\n",
        "               max_num_context,\n",
        "               x_size=1,\n",
        "               y_size=1,\n",
        "               l1_scale=0.6,\n",
        "               sigma_scale=1.0,\n",
        "               random_kernel_parameters=True,\n",
        "               testing=False):\n",
        "    \"\"\"Creates a regression dataset of functions sampled from a GP.\n",
        "\n",
        "    Args:\n",
        "      batch_size: An integer.\n",
        "      max_num_context: The max number of observations in the context.\n",
        "      x_size: Integer >= 1 for length of \"x values\" vector.\n",
        "      y_size: Integer >= 1 for length of \"y values\" vector.\n",
        "      l1_scale: Float; typical scale for kernel distance function.\n",
        "      sigma_scale: Float; typical scale for variance.\n",
        "      random_kernel_parameters: If `True`, the kernel parameters (l1 and sigma) \n",
        "          will be sampled uniformly within [0.1, l1_scale] and [0.1, sigma_scale].\n",
        "      testing: Boolean that indicates whether we are testing. If so there are\n",
        "          more targets for visualization.\n",
        "    \"\"\"\n",
        "    self._batch_size = batch_size\n",
        "    self._max_num_context = max_num_context\n",
        "    self._x_size = x_size\n",
        "    self._y_size = y_size\n",
        "    self._l1_scale = l1_scale\n",
        "    self._sigma_scale = sigma_scale\n",
        "    self._random_kernel_parameters = random_kernel_parameters\n",
        "    self._testing = testing\n",
        "\n",
        "  def _gaussian_kernel(self, xdata, l1, sigma_f, sigma_noise=2e-2):\n",
        "    \"\"\"Applies the Gaussian kernel to generate curve data.\n",
        "\n",
        "    Args:\n",
        "      xdata: Tensor of shape [B, num_total_points, x_size] with\n",
        "          the values of the x-axis data.\n",
        "      l1: Tensor of shape [B, y_size, x_size], the scale\n",
        "          parameter of the Gaussian kernel.\n",
        "      sigma_f: Tensor of shape [B, y_size], the magnitude\n",
        "          of the std.\n",
        "      sigma_noise: Float, std of the noise that we add for stability.\n",
        "\n",
        "    Returns:\n",
        "      The kernel, a float tensor of shape\n",
        "      [B, y_size, num_total_points, num_total_points].\n",
        "    \"\"\"\n",
        "    num_total_points = tf.shape(xdata)[1]\n",
        "\n",
        "    # Expand and take the difference\n",
        "    xdata1 = tf.expand_dims(xdata, axis=1)  # [B, 1, num_total_points, x_size]\n",
        "    xdata2 = tf.expand_dims(xdata, axis=2)  # [B, num_total_points, 1, x_size]\n",
        "    diff = xdata1 - xdata2  # [B, num_total_points, num_total_points, x_size]\n",
        "\n",
        "    # [B, y_size, num_total_points, num_total_points, x_size]\n",
        "    norm = tf.square(diff[:, None, :, :, :] / l1[:, :, None, None, :])\n",
        "\n",
        "    norm = tf.reduce_sum(\n",
        "        norm, -1)  # [B, data_size, num_total_points, num_total_points]\n",
        "\n",
        "    # [B, y_size, num_total_points, num_total_points]\n",
        "    kernel = tf.square(sigma_f)[:, :, None, None] * tf.exp(-0.5 * norm)\n",
        "\n",
        "    # Add some noise to the diagonal to make the cholesky work.\n",
        "    kernel += (sigma_noise**2) * tf.eye(num_total_points)\n",
        "\n",
        "    return kernel\n",
        "\n",
        "  def generate_curves(self):\n",
        "    \"\"\"Builds the op delivering the data.\n",
        "\n",
        "    Generated functions are `float32` with x values between -2 and 2.\n",
        "    \n",
        "    Returns:\n",
        "      A `NPRegressionDescription` namedtuple.\n",
        "    \"\"\"\n",
        "    num_context = tf.random_uniform(\n",
        "        shape=[], minval=3, maxval=self._max_num_context, dtype=tf.int32)\n",
        "\n",
        "    # If we are testing we want to have more targets and have them evenly\n",
        "    # distributed in order to plot the function.\n",
        "    if self._testing:\n",
        "      num_target = 400\n",
        "      num_total_points = num_target\n",
        "      x_values = tf.tile(\n",
        "          tf.expand_dims(tf.range(-2., 2., 1. / 100, dtype=tf.float32), axis=0),\n",
        "          [self._batch_size, 1])\n",
        "      x_values = tf.expand_dims(x_values, axis=-1)\n",
        "    # During training the number of target points and their x-positions are\n",
        "    # selected at random\n",
        "    else:\n",
        "      num_target = tf.random_uniform(shape=(), minval=0, \n",
        "                                     maxval=self._max_num_context - num_context,\n",
        "                                     dtype=tf.int32)\n",
        "      num_total_points = num_context + num_target\n",
        "      x_values = tf.random_uniform(\n",
        "          [self._batch_size, num_total_points, self._x_size], -2, 2)\n",
        "\n",
        "    # Set kernel parameters\n",
        "    # Either choose a set of random parameters for the mini-batch\n",
        "    if self._random_kernel_parameters:\n",
        "      l1 = tf.random_uniform([self._batch_size, self._y_size,\n",
        "                              self._x_size], 0.1, self._l1_scale)\n",
        "      sigma_f = tf.random_uniform([self._batch_size, self._y_size],\n",
        "                                  0.1, self._sigma_scale)\n",
        "    # Or use the same fixed parameters for all mini-batches\n",
        "    else:\n",
        "      l1 = tf.ones(shape=[self._batch_size, self._y_size,\n",
        "                          self._x_size]) * self._l1_scale\n",
        "      sigma_f = tf.ones(shape=[self._batch_size,\n",
        "                               self._y_size]) * self._sigma_scale\n",
        "\n",
        "    # Pass the x_values through the Gaussian kernel\n",
        "    # [batch_size, y_size, num_total_points, num_total_points]\n",
        "    kernel = self._gaussian_kernel(x_values, l1, sigma_f)\n",
        "\n",
        "    # Calculate Cholesky, using double precision for better stability:\n",
        "    cholesky = tf.cast(tf.cholesky(tf.cast(kernel, tf.float64)), tf.float32)\n",
        "\n",
        "    # Sample a curve\n",
        "    # [batch_size, y_size, num_total_points, 1]\n",
        "    y_values = tf.matmul(\n",
        "        cholesky,\n",
        "        tf.random_normal([self._batch_size, self._y_size, num_total_points, 1]))\n",
        "\n",
        "    # [batch_size, num_total_points, y_size]\n",
        "    y_values = tf.transpose(tf.squeeze(y_values, 3), [0, 2, 1])\n",
        "\n",
        "    if self._testing:\n",
        "      # Select the targets\n",
        "      target_x = x_values\n",
        "      target_y = y_values\n",
        "\n",
        "      # Select the observations\n",
        "      idx = tf.random_shuffle(tf.range(num_target))\n",
        "      context_x = tf.gather(x_values, idx[:num_context], axis=1)\n",
        "      context_y = tf.gather(y_values, idx[:num_context], axis=1)\n",
        "\n",
        "    else:\n",
        "      # Select the targets which will consist of the context points as well as\n",
        "      # some new target points\n",
        "      target_x = x_values[:, :num_target + num_context, :]\n",
        "      target_y = y_values[:, :num_target + num_context, :]\n",
        "\n",
        "      # Select the observations\n",
        "      context_x = x_values[:, :num_context, :]\n",
        "      context_y = y_values[:, :num_context, :]\n",
        "\n",
        "    query = ((context_x, context_y), target_x)\n",
        "\n",
        "    return NPRegressionDescription(\n",
        "        query=query,\n",
        "        target_y=target_y,\n",
        "        num_total_points=tf.shape(target_x)[1],\n",
        "        num_context_points=num_context)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "GhMwui0VfmNn",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Attentive Neural Processes: a short introduction\n",
        "\n",
        "Here below are the model diagrams for the **NP** (left) and **ANP** (right).\n",
        "\n",
        "![](https://i.ibb.co/Js1B7RB/model-figure-new-1-page-001.jpg)\n",
        "\n",
        "In the NP, the **context points** $(x_C,y_C)=(x_i, y_i)_{i \\in C}$ are passed through the encoder that consists of two paths, a **deterministic path** and and a **latent path**. \n",
        "\n",
        "In the **deterministic path**, each context pair $(x_i,y_i)$ is passed through an MLP (shared parameters across the contexts) to produce representation $r_i$. These are aggregated by taking the mean to produce the deterministic code $r_C$. \n",
        "\n",
        "In the **latent path**, a code $s_C$ is computed in a similar manner from the representations $s_i$, and is used to parameterise the distribution of the latent variable $z$, giving the latent distribution $q(z|s_C)$.\n",
        "\n",
        "In the decoder, the $r_C$ and $z$ are concatenated alongside $x_*$ and passed through an MLP to produce the parameters of the distribution $p(y_*|x_*,r_C,z)$. \n",
        "\n",
        "The motivation for having a global latent is to model different realisations of the data generating stochastic process - each sample of $z$ would correspond to one realisation of the stochastic process. One can define the model using just the deterministic path, just the latent path, or both.\n",
        "\n",
        "One problem of the NP is that the **mean-aggregation step in the encoder acts as a bottleneck**: since taking the mean across context representations gives the same weight to each context point, it is difficult for the decoder to learn which context points provide relevant information for a given target prediction. \n",
        "\n",
        "This is addressed by ANPs, where the mean-aggregation is replaced by a **cross-attention mechanism** - the target query $x_*$ attends to the key-value pairs $(x_i,r_i)_{i \\in C}$ and assigns weights $w_i$ to each pair to form a query-specific representation $r_*=\\sum_i w_i r_i$. This is precisely where the model allows each query to attend more closely to the context points that it deems relevant for the prediction. Note that if we use uniform attention (all $w_i$ equal), then we revert to the NP.\n",
        "\n",
        "Another change is the **self-attention mechanism** that replaces the MLPs in the encoder, used in order to model interactions between the context points. However for the 1D regression task here, we do not use self-attention and resort to the MLP setting as it is shown to be sufficient, and just use cross-attention.\n",
        "\n",
        "Learning for both the NP and ANP is done by optimising the ELBO to the log predictive likelihood:\n",
        "\n",
        "$$\\log p(y_T|x_T,x_C,y_C)  \\geq\n",
        "\\mathbb{E}_{q(z|s_T)}  [\\log p(y_T|x_T,r_C,z)] - KL ( q(z|s_T) \\Vert q(z|s_C) )$$\n",
        "where $C$ represents contexts and $T$ represents targets."
      ]
    },
    {
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        "id": "ps97odopnvkv",
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        "colab": {}
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      "cell_type": "code",
      "source": [
        "# utility methods\n",
        "def batch_mlp(input, output_sizes, variable_scope):\n",
        "  \"\"\"Apply MLP to the final axis of a 3D tensor (reusing already defined MLPs).\n",
        "  \n",
        "  Args:\n",
        "    input: input tensor of shape [B,n,d_in].\n",
        "    output_sizes: An iterable containing the output sizes of the MLP as defined \n",
        "        in `basic.Linear`.\n",
        "    variable_scope: String giving the name of the variable scope. If this is set\n",
        "        to be the same as a previously defined MLP, then the weights are reused.\n",
        "    \n",
        "  Returns:\n",
        "    tensor of shape [B,n,d_out] where d_out=output_sizes[-1]\n",
        "  \"\"\"\n",
        "  # Get the shapes of the input and reshape to parallelise across observations\n",
        "  batch_size, _, filter_size = input.shape.as_list()\n",
        "  output = tf.reshape(input, (-1, filter_size))\n",
        "  output.set_shape((None, filter_size))\n",
        "\n",
        "  # Pass through MLP\n",
        "  with tf.variable_scope(variable_scope, reuse=tf.AUTO_REUSE):\n",
        "    for i, size in enumerate(output_sizes[:-1]):\n",
        "      output = tf.nn.relu(\n",
        "          tf.layers.dense(output, size, name=\"layer_{}\".format(i)))\n",
        "\n",
        "    # Last layer without a ReLu\n",
        "    output = tf.layers.dense(\n",
        "        output, output_sizes[-1], name=\"layer_{}\".format(i + 1))\n",
        "\n",
        "  # Bring back into original shape\n",
        "  output = tf.reshape(output, (batch_size, -1, output_sizes[-1]))\n",
        "  return output"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "kli9cfXqt2Jf",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Encoder: Deterministic Path\n",
        "\n",
        "The encoder in the deterministic path is shared between all context pairs and consists of an MLP and an attention module. Each context $x_i$ and $y_i$ are concatenated and passed through the MLP (with relu non-linearities) to output a representation $r_i$. These $(r_i)_{i \\in C}$ and $x_i$ are fed into the cross-attention module, along with query $x_*$ to output a query-specific representation $r_*$. The MLP architecture is given by the `output_sizes` argument, a list of hidden layer sizes, and the `attention` argument which is the cross-attention module defined later on."
      ]
    },
    {
      "metadata": {
        "id": "yXdB68gkPwy2",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "class DeterministicEncoder(object):\n",
        "  \"\"\"The Deterministic Encoder.\"\"\"\n",
        "\n",
        "  def __init__(self, output_sizes, attention):\n",
        "    \"\"\"(A)NP deterministic encoder.\n",
        "\n",
        "    Args:\n",
        "      output_sizes: An iterable containing the output sizes of the encoding MLP.\n",
        "      attention: The attention module.\n",
        "    \"\"\"\n",
        "    self._output_sizes = output_sizes\n",
        "    self._attention = attention\n",
        "\n",
        "  def __call__(self, context_x, context_y, target_x):\n",
        "    \"\"\"Encodes the inputs into one representation.\n",
        "\n",
        "    Args:\n",
        "      context_x: Tensor of shape [B,observations,d_x]. For this 1D regression\n",
        "          task this corresponds to the x-values.\n",
        "      context_y: Tensor of shape [B,observations,d_y]. For this 1D regression\n",
        "          task this corresponds to the y-values.\n",
        "      target_x: Tensor of shape [B,target_observations,d_x]. \n",
        "          For this 1D regression task this corresponds to the x-values.\n",
        "\n",
        "    Returns:\n",
        "      The encoded representation. Tensor of shape [B,target_observations,d]\n",
        "    \"\"\"\n",
        "\n",
        "    # Concatenate x and y along the filter axes\n",
        "    encoder_input = tf.concat([context_x, context_y], axis=-1)\n",
        "\n",
        "    # Pass final axis through MLP\n",
        "    hidden = batch_mlp(encoder_input, self._output_sizes, \n",
        "                       \"deterministic_encoder\")\n",
        "\n",
        "    # Apply attention\n",
        "    with tf.variable_scope(\"deterministic_encoder\", reuse=tf.AUTO_REUSE):\n",
        "        hidden = self._attention(context_x, target_x, hidden)\n",
        "\n",
        "    return hidden\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "1944scGst6fS",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Encoder: Latent Path\n",
        "\n",
        "The encoder in the latent path is again shared by all context pairs and consists of an MLP.  After the MLP (with relu non-linearities) is applied the resulting representation is aggregated by taking the mean across the contexts and a further MLP is applied to compute the mean and variance of the Gaussian $q(z|s_C)$. Again the initial MLP's architecture is given by the `output_sizes` argument, and the `num_latent` argument sets the latent dimensionality."
      ]
    },
    {
      "metadata": {
        "id": "gufhxfGSRCs9",
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        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "class LatentEncoder(object):\n",
        "  \"\"\"The Latent Encoder.\"\"\"\n",
        "\n",
        "  def __init__(self, output_sizes, num_latents):\n",
        "    \"\"\"(A)NP latent encoder.\n",
        "\n",
        "    Args:\n",
        "      output_sizes: An iterable containing the output sizes of the encoding MLP.\n",
        "      num_latents: The latent dimensionality.\n",
        "    \"\"\"\n",
        "    self._output_sizes = output_sizes\n",
        "    self._num_latents = num_latents\n",
        "\n",
        "  def __call__(self, x, y):\n",
        "    \"\"\"Encodes the inputs into one representation.\n",
        "\n",
        "    Args:\n",
        "      x: Tensor of shape [B,observations,d_x]. For this 1D regression\n",
        "          task this corresponds to the x-values.\n",
        "      y: Tensor of shape [B,observations,d_y]. For this 1D regression\n",
        "          task this corresponds to the y-values.\n",
        "\n",
        "    Returns:\n",
        "      A normal distribution over tensors of shape [B, num_latents]\n",
        "    \"\"\"\n",
        "\n",
        "    # Concatenate x and y along the filter axes\n",
        "    encoder_input = tf.concat([x, y], axis=-1)\n",
        "\n",
        "    # Pass final axis through MLP\n",
        "    hidden = batch_mlp(encoder_input, self._output_sizes, \"latent_encoder\")\n",
        "      \n",
        "    # Aggregator: take the mean over all points\n",
        "    hidden = tf.reduce_mean(hidden, axis=1)\n",
        "    \n",
        "    # Have further MLP layers that map to the parameters of the Gaussian latent\n",
        "    with tf.variable_scope(\"latent_encoder\", reuse=tf.AUTO_REUSE):\n",
        "      # First apply intermediate relu layer \n",
        "      hidden = tf.nn.relu(\n",
        "          tf.layers.dense(hidden, \n",
        "                          (self._output_sizes[-1] + self._num_latents)/2, \n",
        "                          name=\"penultimate_layer\"))\n",
        "      # Then apply further linear layers to output latent mu and log sigma\n",
        "      mu = tf.layers.dense(hidden, self._num_latents, name=\"mean_layer\")\n",
        "      log_sigma = tf.layers.dense(hidden, self._num_latents, name=\"std_layer\")\n",
        "      \n",
        "    # Compute sigma\n",
        "    sigma = 0.1 + 0.9 * tf.sigmoid(log_sigma)\n",
        "\n",
        "    return tf.contrib.distributions.Normal(loc=mu, scale=sigma)\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "roGKUH3Nt9Xg",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Decoder\n",
        "\n",
        "The context representation (either $z$ or $z$ and $r_C$ concatenated) and the target inputs $x_T$ are fed into the decoder. First they are concatenated and passed through an MLP, whose architecture is given by the `output_sizes` argument. The MLP outputs the mean and variance of the Gaussian $p(y_T|x_T,r_C,z)$. "
      ]
    },
    {
      "metadata": {
        "id": "RLhx-J8ALyST",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "class Decoder(object):\n",
        "  \"\"\"The Decoder.\"\"\"\n",
        "\n",
        "  def __init__(self, output_sizes):\n",
        "    \"\"\"(A)NP decoder.\n",
        "\n",
        "    Args:\n",
        "      output_sizes: An iterable containing the output sizes of the decoder MLP \n",
        "          as defined in `basic.Linear`.\n",
        "    \"\"\"\n",
        "    self._output_sizes = output_sizes\n",
        "\n",
        "  def __call__(self, representation, target_x):\n",
        "    \"\"\"Decodes the individual targets.\n",
        "\n",
        "    Args:\n",
        "      representation: The representation of the context for target predictions. \n",
        "          Tensor of shape [B,target_observations,?].\n",
        "      target_x: The x locations for the target query.\n",
        "          Tensor of shape [B,target_observations,d_x].\n",
        "\n",
        "    Returns:\n",
        "      dist: A multivariate Gaussian over the target points. A distribution over\n",
        "          tensors of shape [B,target_observations,d_y].\n",
        "      mu: The mean of the multivariate Gaussian.\n",
        "          Tensor of shape [B,target_observations,d_x].\n",
        "      sigma: The standard deviation of the multivariate Gaussian.\n",
        "          Tensor of shape [B,target_observations,d_x].\n",
        "    \"\"\"\n",
        "    # concatenate target_x and representation\n",
        "    hidden = tf.concat([representation, target_x], axis=-1)\n",
        "    \n",
        "    # Pass final axis through MLP\n",
        "    hidden = batch_mlp(hidden, self._output_sizes, \"decoder\")\n",
        "\n",
        "    # Get the mean an the variance\n",
        "    mu, log_sigma = tf.split(hidden, 2, axis=-1)\n",
        "\n",
        "    # Bound the variance\n",
        "    sigma = 0.1 + 0.9 * tf.nn.softplus(log_sigma)\n",
        "\n",
        "    # Get the distribution\n",
        "    dist = tf.contrib.distributions.MultivariateNormalDiag(\n",
        "        loc=mu, scale_diag=sigma)\n",
        "\n",
        "    return dist, mu, sigma"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "bOfbRLHpt_KK",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Model\n",
        "\n",
        "We can put the encoders and the decoder together to form the ANP model."
      ]
    },
    {
      "metadata": {
        "id": "n5XJ6gr7ZDPl",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "class LatentModel(object):\n",
        "  \"\"\"The (A)NP model.\"\"\"\n",
        "\n",
        "  def __init__(self, latent_encoder_output_sizes, num_latents,\n",
        "               decoder_output_sizes, use_deterministic_path=True, \n",
        "               deterministic_encoder_output_sizes=None, attention=None):\n",
        "    \"\"\"Initialises the model.\n",
        "\n",
        "    Args:\n",
        "      latent_encoder_output_sizes: An iterable containing the sizes of hidden \n",
        "          layers of the latent encoder.\n",
        "      num_latents: The latent dimensionality.\n",
        "      decoder_output_sizes: An iterable containing the sizes of hidden layers of\n",
        "          the decoder. The last element should correspond to d_y * 2\n",
        "          (it encodes both mean and variance concatenated)\n",
        "      use_deterministic_path: a boolean that indicates whether the deterministic\n",
        "          encoder is used or not.\n",
        "      deterministic_encoder_output_sizes: An iterable containing the sizes of \n",
        "          hidden layers of the deterministic encoder. The last one is the size \n",
        "          of the deterministic representation r.\n",
        "      attention: The attention module used in the deterministic encoder.\n",
        "          Only relevant when use_deterministic_path=True.\n",
        "    \"\"\"\n",
        "    self._latent_encoder = LatentEncoder(latent_encoder_output_sizes, \n",
        "                                         num_latents)\n",
        "    self._decoder = Decoder(decoder_output_sizes)\n",
        "    self._use_deterministic_path = use_deterministic_path\n",
        "    if use_deterministic_path:\n",
        "      self._deterministic_encoder = DeterministicEncoder(\n",
        "          deterministic_encoder_output_sizes, attention)\n",
        "    \n",
        "\n",
        "  def __call__(self, query, num_targets, target_y=None):\n",
        "    \"\"\"Returns the predicted mean and variance at the target points.\n",
        "\n",
        "    Args:\n",
        "      query: Array containing ((context_x, context_y), target_x) where:\n",
        "          context_x: Tensor of shape [B,num_contexts,d_x]. \n",
        "              Contains the x values of the context points.\n",
        "          context_y: Tensor of shape [B,num_contexts,d_y]. \n",
        "              Contains the y values of the context points.\n",
        "          target_x: Tensor of shape [B,num_targets,d_x]. \n",
        "              Contains the x values of the target points.\n",
        "      num_targets: Number of target points.\n",
        "      target_y: The ground truth y values of the target y. \n",
        "          Tensor of shape [B,num_targets,d_y].\n",
        "\n",
        "    Returns:\n",
        "      log_p: The log_probability of the target_y given the predicted\n",
        "          distribution. Tensor of shape [B,num_targets].\n",
        "      mu: The mean of the predicted distribution. \n",
        "          Tensor of shape [B,num_targets,d_y].\n",
        "      sigma: The variance of the predicted distribution.\n",
        "          Tensor of shape [B,num_targets,d_y].\n",
        "    \"\"\"\n",
        "\n",
        "    (context_x, context_y), target_x = query\n",
        "\n",
        "    # Pass query through the encoder and the decoder\n",
        "    prior = self._latent_encoder(context_x, context_y)\n",
        "    \n",
        "    # For training, when target_y is available, use targets for latent encoder.\n",
        "    # Note that targets contain contexts by design.\n",
        "    if target_y is None:\n",
        "      latent_rep = prior.sample()\n",
        "    # For testing, when target_y unavailable, use contexts for latent encoder.\n",
        "    else:\n",
        "      posterior = self._latent_encoder(target_x, target_y)\n",
        "      latent_rep = posterior.sample()\n",
        "    latent_rep = tf.tile(tf.expand_dims(latent_rep, axis=1),\n",
        "                         [1, num_targets, 1])\n",
        "    if self._use_deterministic_path:\n",
        "      deterministic_rep = self._deterministic_encoder(context_x, context_y,\n",
        "                                                      target_x)\n",
        "      representation = tf.concat([deterministic_rep, latent_rep], axis=-1)\n",
        "    else:\n",
        "      representation = latent_rep\n",
        "      \n",
        "    dist, mu, sigma = self._decoder(representation, target_x)\n",
        "    \n",
        "    # If we want to calculate the log_prob for training we will make use of the\n",
        "    # target_y. At test time the target_y is not available so we return None.\n",
        "    if target_y is not None:\n",
        "      log_p = dist.log_prob(target_y)\n",
        "      posterior = self._latent_encoder(target_x, target_y)\n",
        "      kl = tf.reduce_sum(\n",
        "          tf.contrib.distributions.kl_divergence(posterior, prior), \n",
        "          axis=-1, keepdims=True)\n",
        "      kl = tf.tile(kl, [1, num_targets])\n",
        "      loss = - tf.reduce_mean(log_p - kl / tf.cast(num_targets, tf.float32))\n",
        "    else:\n",
        "      log_p = None\n",
        "      kl = None\n",
        "      loss = None\n",
        "\n",
        "    return mu, sigma, log_p, kl, loss\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "ULaa6hZEuHvU",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Cross-Attention Module\n",
        "Given a set of key-value pairs $(k_i,v_i)_{i \\in I}$ and query $q$, an attention module computes weights for each key and aggregates the values with these weights to form the value corresponding to the query.\n",
        "\n",
        "\n",
        "**`rep`** determines whether the raw inputs to the module will be used as the keys and queries, or whether you will pass them through an MLP and use the output instead. One of 'identity', 'mlp'.\n",
        "\n",
        "**`output_sizes`** determines the architecture of the MLP used to obtain the keys/queries if `rep` is 'mlp'.\n",
        "\n",
        "**`att_type`** is a string argument that determines the type of attention used. Valid choices of attention are: uniform, laplace, dot product, multihead.\n",
        "\n",
        "* **Uniform** $((k_i,v_i)_{i\\in I}, q)= \\frac{1}{|I|} \\sum_i v_i$\n",
        "\n",
        "* **Laplace** $((k_i,v_i)_{i\\in I}, q)= \\sum_i w_i v_i, \\hspace{2mm} w_i \\propto \\exp(-\\frac{||q - k_i||_1}{l})$\n",
        "\n",
        "* **DotProduct** $((k_i,v_i)_{i\\in I}, q)= \\sum_i w_i v_i, \\hspace{2mm} w_i \\propto \\exp(q^\\top k_i / \\sqrt{d_k})$ where $k_i \\in \\mathbb{R}^{d_k}$.\n",
        "\n",
        "* **Multihead** $((k_i,v_i)_{i\\in I}, q)= \\mathcal{L}^O(\\text{concat}(\\text{head}_1, \\ldots, \\text{head}_H))$, $\\text{head}_h = \\text{DotProduct}((\\mathcal{L}^K_h(k_i),\\mathcal{L}^V_h(v_i))_{i \\in I}, \\mathcal{L}^Q_h(q))$ \n",
        "\n",
        "  where $\\mathcal{L}$ are linear maps with trainable parameters.\n",
        "\n",
        "**`scale`**: length scale $l$ in Laplace attention.\n",
        "\n",
        "**`normalise`**: whether to use a softmax so that weights sum to 1 or not.\n",
        "\n",
        "**`num_heads`**: $H$, the number of heads for multihead attention."
      ]
    },
    {
      "metadata": {
        "id": "DImJP8HfhmmM",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def uniform_attention(q, v):\n",
        "  \"\"\"Uniform attention. Equivalent to np.\n",
        "\n",
        "  Args:\n",
        "    q: queries. tensor of shape [B,m,d_k].\n",
        "    v: values. tensor of shape [B,n,d_v].\n",
        "    \n",
        "  Returns:\n",
        "    tensor of shape [B,m,d_v].\n",
        "  \"\"\"\n",
        "  total_points = tf.shape(q)[1]\n",
        "  rep = tf.reduce_mean(v, axis=1, keepdims=True)  # [B,1,d_v]\n",
        "  rep = tf.tile(rep, [1, total_points, 1])\n",
        "  return rep\n",
        "\n",
        "def laplace_attention(q, k, v, scale, normalise):\n",
        "  \"\"\"Computes laplace exponential attention.\n",
        "\n",
        "  Args:\n",
        "    q: queries. tensor of shape [B,m,d_k].\n",
        "    k: keys. tensor of shape [B,n,d_k].\n",
        "    v: values. tensor of shape [B,n,d_v].\n",
        "    scale: float that scales the L1 distance.\n",
        "    normalise: Boolean that determines whether weights sum to 1.\n",
        "    \n",
        "  Returns:\n",
        "    tensor of shape [B,m,d_v].\n",
        "  \"\"\"\n",
        "  k = tf.expand_dims(k, axis=1)  # [B,1,n,d_k]\n",
        "  q = tf.expand_dims(q, axis=2)  # [B,m,1,d_k]\n",
        "  unnorm_weights = - tf.abs((k - q) / scale)  # [B,m,n,d_k]\n",
        "  unnorm_weights = tf.reduce_sum(unnorm_weights, axis=-1)  # [B,m,n]\n",
        "  if normalise:\n",
        "    weight_fn = tf.nn.softmax\n",
        "  else:\n",
        "    weight_fn = lambda x: 1 + tf.tanh(x)\n",
        "  weights = weight_fn(unnorm_weights)  # [B,m,n]\n",
        "  rep = tf.einsum('bik,bkj->bij', weights, v)  # [B,m,d_v]\n",
        "  return rep\n",
        "\n",
        "\n",
        "def dot_product_attention(q, k, v, normalise):\n",
        "  \"\"\"Computes dot product attention.\n",
        "\n",
        "  Args:\n",
        "    q: queries. tensor of  shape [B,m,d_k].\n",
        "    k: keys. tensor of shape [B,n,d_k].\n",
        "    v: values. tensor of shape [B,n,d_v].\n",
        "    normalise: Boolean that determines whether weights sum to 1.\n",
        "    \n",
        "  Returns:\n",
        "    tensor of shape [B,m,d_v].\n",
        "  \"\"\"\n",
        "  d_k = tf.shape(q)[-1]\n",
        "  scale = tf.sqrt(tf.cast(d_k, tf.float32))\n",
        "  unnorm_weights = tf.einsum('bjk,bik->bij', k, q) / scale  # [B,m,n]\n",
        "  if normalise:\n",
        "    weight_fn = tf.nn.softmax\n",
        "  else:\n",
        "    weight_fn = tf.sigmoid\n",
        "  weights = weight_fn(unnorm_weights)  # [B,m,n]\n",
        "  rep = tf.einsum('bik,bkj->bij', weights, v)  # [B,m,d_v]\n",
        "  return rep\n",
        "\n",
        "\n",
        "def multihead_attention(q, k, v, num_heads=8):\n",
        "  \"\"\"Computes multi-head attention.\n",
        "\n",
        "  Args:\n",
        "    q: queries. tensor of  shape [B,m,d_k].\n",
        "    k: keys. tensor of shape [B,n,d_k].\n",
        "    v: values. tensor of shape [B,n,d_v].\n",
        "    num_heads: number of heads. Should divide d_v.\n",
        "    \n",
        "  Returns:\n",
        "    tensor of shape [B,m,d_v].\n",
        "  \"\"\"\n",
        "  d_k = q.get_shape().as_list()[-1]\n",
        "  d_v = v.get_shape().as_list()[-1]\n",
        "  head_size = d_v / num_heads\n",
        "  key_initializer = tf.random_normal_initializer(stddev=d_k**-0.5)\n",
        "  value_initializer = tf.random_normal_initializer(stddev=d_v**-0.5)\n",
        "  rep = tf.constant(0.0)\n",
        "  for h in range(num_heads):\n",
        "    o = dot_product_attention(\n",
        "        tf.layers.Conv1D(head_size, 1, kernel_initializer=key_initializer,\n",
        "                   name='wq%d' % h, use_bias=False, padding='VALID')(q),\n",
        "        tf.layers.Conv1D(head_size, 1, kernel_initializer=key_initializer,\n",
        "                   name='wk%d' % h, use_bias=False, padding='VALID')(k),\n",
        "        tf.layers.Conv1D(head_size, 1, kernel_initializer=key_initializer,\n",
        "                   name='wv%d' % h, use_bias=False, padding='VALID')(v),\n",
        "        normalise=True)\n",
        "    rep += tf.layers.Conv1D(d_v, 1, kernel_initializer=value_initializer,\n",
        "                      name='wo%d' % h, use_bias=False, padding='VALID')(o)\n",
        "  return rep\n",
        "\n",
        "class Attention(object):\n",
        "  \"\"\"The Attention module.\"\"\"\n",
        "\n",
        "  def __init__(self, rep, output_sizes, att_type, scale=1., normalise=True,\n",
        "               num_heads=8):\n",
        "    \"\"\"Create attention module.\n",
        "\n",
        "    Takes in context inputs, target inputs and\n",
        "    representations of each context input/output pair\n",
        "    to output an aggregated representation of the context data.\n",
        "    Args:\n",
        "      rep: transformation to apply to contexts before computing attention. \n",
        "          One of: ['identity','mlp'].\n",
        "      output_sizes: list of number of hidden units per layer of mlp.\n",
        "          Used only if rep == 'mlp'.\n",
        "      att_type: type of attention. One of the following:\n",
        "          ['uniform','laplace','dot_product','multihead']\n",
        "      scale: scale of attention.\n",
        "      normalise: Boolean determining whether to:\n",
        "          1. apply softmax to weights so that they sum to 1 across context pts or\n",
        "          2. apply custom transformation to have weights in [0,1].\n",
        "      num_heads: number of heads for multihead.\n",
        "    \"\"\"\n",
        "    self._rep = rep\n",
        "    self._output_sizes = output_sizes\n",
        "    self._type = att_type\n",
        "    self._scale = scale\n",
        "    self._normalise = normalise\n",
        "    if self._type == 'multihead':\n",
        "      self._num_heads = num_heads\n",
        "\n",
        "  def __call__(self, x1, x2, r):\n",
        "    \"\"\"Apply attention to create aggregated representation of r.\n",
        "\n",
        "    Args:\n",
        "      x1: tensor of shape [B,n1,d_x].\n",
        "      x2: tensor of shape [B,n2,d_x].\n",
        "      r: tensor of shape [B,n1,d].\n",
        "      \n",
        "    Returns:\n",
        "      tensor of shape [B,n2,d]\n",
        "\n",
        "    Raises:\n",
        "      NameError: The argument for rep/type was invalid.\n",
        "    \"\"\"\n",
        "    if self._rep == 'identity':\n",
        "      k, q = (x1, x2)\n",
        "    elif self._rep == 'mlp':\n",
        "      # Pass through MLP\n",
        "      k = batch_mlp(x1, self._output_sizes, \"attention\")\n",
        "      q = batch_mlp(x2, self._output_sizes, \"attention\")\n",
        "    else:\n",
        "      raise NameError(\"'rep' not among ['identity','mlp']\")\n",
        "\n",
        "    if self._type == 'uniform':\n",
        "      rep = uniform_attention(q, r)\n",
        "    elif self._type == 'laplace':\n",
        "      rep = laplace_attention(q, k, r, self._scale, self._normalise)\n",
        "    elif self._type == 'dot_product':\n",
        "      rep = dot_product_attention(q, k, r, self._normalise)\n",
        "    elif self._type == 'multihead':\n",
        "      rep = multihead_attention(q, k, r, self._num_heads)\n",
        "    else:\n",
        "      raise NameError((\"'att_type' not among ['uniform','laplace','dot_product'\"\n",
        "                       \",'multihead']\"))\n",
        "\n",
        "    return rep"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "zYcTQDLltFmA",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Ploting function\n",
        "\n",
        "Same plotting function as for the [implementation of CNPs](https://github.com/deepmind/conditional-neural-process/blob/master/conditional_neural_process.ipynb) that plots the intermediate predictions every so often during training."
      ]
    },
    {
      "metadata": {
        "id": "AFlT3lJQTM_m",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def plot_functions(target_x, target_y, context_x, context_y, pred_y, std):\n",
        "  \"\"\"Plots the predicted mean and variance and the context points.\n",
        "  \n",
        "  Args: \n",
        "    target_x: An array of shape [B,num_targets,1] that contains the\n",
        "        x values of the target points.\n",
        "    target_y: An array of shape [B,num_targets,1] that contains the\n",
        "        y values of the target points.\n",
        "    context_x: An array of shape [B,num_contexts,1] that contains \n",
        "        the x values of the context points.\n",
        "    context_y: An array of shape [B,num_contexts,1] that contains \n",
        "        the y values of the context points.\n",
        "    pred_y: An array of shape [B,num_targets,1] that contains the\n",
        "        predicted means of the y values at the target points in target_x.\n",
        "    std: An array of shape [B,num_targets,1] that contains the\n",
        "        predicted std dev of the y values at the target points in target_x.\n",
        "  \"\"\"\n",
        "  # Plot everything\n",
        "  plt.plot(target_x[0], pred_y[0], 'b', linewidth=2)\n",
        "  plt.plot(target_x[0], target_y[0], 'k:', linewidth=2)\n",
        "  plt.plot(context_x[0], context_y[0], 'ko', markersize=10)\n",
        "  plt.fill_between(\n",
        "      target_x[0, :, 0],\n",
        "      pred_y[0, :, 0] - std[0, :, 0],\n",
        "      pred_y[0, :, 0] + std[0, :, 0],\n",
        "      alpha=0.2,\n",
        "      facecolor='#65c9f7',\n",
        "      interpolate=True)\n",
        "\n",
        "  # Make the plot pretty\n",
        "  plt.yticks([-2, 0, 2], fontsize=16)\n",
        "  plt.xticks([-2, 0, 2], fontsize=16)\n",
        "  plt.ylim([-2, 2])\n",
        "  plt.grid('off')\n",
        "  ax = plt.gca()\n",
        "  plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "Z69Ham1nteeD",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Training the (A)NP\n",
        "\n",
        "We can now start training. First we need to define some variables:\n",
        "\n",
        "**`TRAINING_ITERATIONS`**: Number of iterations used for trianing. At each iteration we sample a new batch of sample curves from GPs and pick a random set of points on each curve to be the target and a subset to be the context. We optimise the ELBO on the log predictive likelihood of the target given context.\n",
        "\n",
        "**`MAX_CONTEXT_POINTS`**: Maximum number of context points used during training. This is also set to be the upper bound on the number of target points.\n",
        "\n",
        "**`PLOT_AFTER`**: The number of iterations between the intermediate plots.\n",
        "\n",
        "**`HIDDEN_SIZE`**: Master parameter that governs the hidden layer size of all MLPs in the model and also the latent dimensionality. \n",
        "\n",
        "**`MODEL_TYPE`**: 'NP' or 'ANP'.\n",
        "\n",
        "**`ATTENTION_TYPE`**: The type of attention used for ANP. One of `uniform`, `laplace` `dot_product` or `multihead`\n",
        "\n",
        "**`random_kernel_parameters`**: Boolean to determine whether the GP kernel parameters are sample randomly for each iteration or fixed.\n"
      ]
    },
    {
      "metadata": {
        "id": "yHqnv8FP4Rtu",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### NP training\n",
        "First we train the NP. Notice from the plots that the predictions after 1e5 iterations do not go through the context points perfectly - i.e. underfits."
      ]
    },
    {
      "metadata": {
        "id": "c6FcSLfnLD9_",
        "colab_type": "code",
        "outputId": "8b1ecc7c-5218-4f7f-b596-a833ecfbd8b7",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1551095030039,
          "user_tz": 0,
          "elapsed": 493150,
          "user": {
            "displayName": "Hyunjik Kim",
            "photoUrl": "https://lh5.googleusercontent.com/-oMZCZLTka34/AAAAAAAAAAI/AAAAAAAAAAc/ENlUKunKSqo/s64/photo.jpg",
            "userId": "01465310974685628261"
          }
        },
        "colab": {
          "height": 2897
        }
      },
      "cell_type": "code",
      "source": [
        "TRAINING_ITERATIONS = 100000 #@param {type:\"number\"}\n",
        "MAX_CONTEXT_POINTS = 50 #@param {type:\"number\"}\n",
        "PLOT_AFTER = 10000 #@param {type:\"number\"}\n",
        "HIDDEN_SIZE = 128 #@param {type:\"number\"}\n",
        "MODEL_TYPE = 'NP' #@param ['NP','ANP']\n",
        "ATTENTION_TYPE = 'uniform' #@param ['uniform','laplace','dot_product','multihead']\n",
        "random_kernel_parameters=True #@param {type:\"boolean\"}\n",
        "\n",
        "tf.reset_default_graph()\n",
        "# Train dataset\n",
        "dataset_train = GPCurvesReader(\n",
        "    batch_size=16, max_num_context=MAX_CONTEXT_POINTS, random_kernel_parameters=random_kernel_parameters)\n",
        "data_train = dataset_train.generate_curves()\n",
        "\n",
        "# Test dataset\n",
        "dataset_test = GPCurvesReader(\n",
        "    batch_size=1, max_num_context=MAX_CONTEXT_POINTS, testing=True, random_kernel_parameters=random_kernel_parameters)\n",
        "data_test = dataset_test.generate_curves()\n",
        "\n",
        "\n",
        "# Sizes of the layers of the MLPs for the encoders and decoder\n",
        "# The final output layer of the decoder outputs two values, one for the mean and\n",
        "# one for the variance of the prediction at the target location\n",
        "latent_encoder_output_sizes = [HIDDEN_SIZE]*4\n",
        "num_latents = HIDDEN_SIZE\n",
        "deterministic_encoder_output_sizes= [HIDDEN_SIZE]*4\n",
        "decoder_output_sizes = [HIDDEN_SIZE]*2 + [2]\n",
        "use_deterministic_path = True\n",
        "\n",
        "\n",
        "# ANP with multihead attention\n",
        "if MODEL_TYPE == 'ANP':\n",
        "  attention = Attention(rep='mlp', output_sizes=[HIDDEN_SIZE]*2, \n",
        "                        att_type=ATTENTION_TYPE)\n",
        "# NP - equivalent to uniform attention\n",
        "elif MODEL_TYPE == 'NP':\n",
        "  attention = Attention(rep='identity', output_sizes=None, att_type='uniform')\n",
        "else:\n",
        "  raise NameError(\"MODEL_TYPE not among ['ANP,'NP']\")\n",
        "\n",
        "# Define the model\n",
        "model = LatentModel(latent_encoder_output_sizes, num_latents,\n",
        "                    decoder_output_sizes, use_deterministic_path, \n",
        "                    deterministic_encoder_output_sizes, attention)\n",
        "\n",
        "# Define the loss\n",
        "_, _, log_prob, _, loss = model(data_train.query, data_train.num_total_points,\n",
        "                                 data_train.target_y)\n",
        "\n",
        "# Get the predicted mean and variance at the target points for the testing set\n",
        "mu, sigma, _, _, _ = model(data_test.query, data_test.num_total_points)\n",
        "\n",
        "# Set up the optimizer and train step\n",
        "optimizer = tf.train.AdamOptimizer(1e-4)\n",
        "train_step = optimizer.minimize(loss)\n",
        "init = tf.initialize_all_variables()\n",
        "\n",
        "# Train and plot\n",
        "with tf.Session() as sess:\n",
        "  sess.run(init)\n",
        "\n",
        "  for it in range(TRAINING_ITERATIONS):\n",
        "    sess.run([train_step])\n",
        "\n",
        "    # Plot the predictions in `PLOT_AFTER` intervals\n",
        "    if it % PLOT_AFTER == 0:\n",
        "      loss_value, pred_y, std_y, target_y, whole_query = sess.run(\n",
        "          [loss, mu, sigma, data_test.target_y, \n",
        "           data_test.query])\n",
        "\n",
        "      (context_x, context_y), target_x = whole_query\n",
        "      print('Iteration: {}, loss: {}'.format(it, loss_value))\n",
        "\n",
        "      # Plot the prediction and the context\n",
        "      plot_functions(target_x, target_y, context_x, context_y, pred_y, std_y)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration: 0, loss: 1.0364459753\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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X1p/xSkwksq9mCn4vR2C3C9Xpk3stC53v70azkYnNevyJZ6x6Ecbxk2cKfo+L51LRo/eD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\nnboIcg+x2Pqy3U2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U0NLm+vvvc/D29kbHjp1Eub8hW7b8ilOnTmDatJktio9lWUyY8ALO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\nyYAQQggoGRBCCAHwf2+NbzInLFFHAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f90285a7ad0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 10000, loss: 0.254928678274\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AURQ2jhHVIPXNldi8cS3mLHgB190wNNDJaTQc04lnHD8GWfJuOu1rEwdj4dLX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\nYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f5cfbf490>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 20000, loss: 0.0929502248764\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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UJikYDLJp0yaSkpJITU2tdf2YhMG6devw+/1s27aNn/70pxGPpaSk\nsGrVqli8rIiIHKOYhMHkyZOZPHlyLDYtIiIxoFFLRUQE+7Rp06Y19k7Uxu12M2TIENxud2PvikgE\nfTelKavL9zOmXUtFRKR5UDWRiIgoDEREJEa9iWJFM6hJU5CRkcGMGTNYs2YNlmUxbNgwHn74YV14\nJo1u+fLlLFu2jC1btpCdnU1ycjKjR49mwoQJxMfH1/jcZtVmsHjxYv79738zduzYiBnUtm7dqhnU\npEF4vV6uuOIK3G43v/zlLwGYNWsWxcXFLF26FI/H08h7KCezcePGkZKSQlpaGklJSWzdupU5c+bQ\ns2dPlixZUvOTrWbk8OHDlZYdOXLEOuuss6yHHnqoEfZITjYLFiyw+vXrZ+3Zs6d02d69e61+/fpZ\nL7zwQuPtmIhlWTk5OZWWvfbaa1bfvn2ttWvX1vjcZtVmoBnUpLGtXr2aQYMGRQzFnpqayuDBg3Vl\nvTS6Nm3aVFo2YMAALMuqtYxsVmFQFc2gJg1p586dnHrqqZWW9+rVi127djXCHonUbP369RiGUWsZ\n2ezDQDOoSUPKzc0lMTGx0vLExMRKI+6KNLbMzEzmzJnDsGHD6N+/f43rNmpvIs2gJs2RYVSeaMlq\nPv0w5CRRWFjIpEmTcDqdzJgxo9b1GzUMGmoGNZH6kpiYSG5ubqXl+fn5VQ6/LtIYfD4fEydOZP/+\n/SxevJhOnTrV+pxGDQO320337t3r/LzXX3+dxx57jNtuu43bb789BnsmUrVevXqxc+fOSst37typ\nditpEgKBAJMnT2bLli0sWLCAXr16RfW8ZtdmsHLlSh555BGuvfbaqKbSFKlPI0eOZPPmzezbt690\n2b59+/jss89IS0trxD0TCVVXTpkyhXXr1jFv3jwGDhwY9XOb1UVnGzZs4LbbbqNXr1785je/wWYr\ny7KaZlATqS9FRUWMGTMGt9vNPffcA8Ds2bMpKirijTfeqLJKU6ShPProo7z00ktMmjSJESNGRDyW\nlJRUY3VRswqDuXPn8te//rXKxzSDmjSUqoajmDp1KikpKY29a3KSGzlyJOnp6VU+duedd9Y46Viz\nCgMREYmNZtdmICIi9U9hICIiCgMREVEYiIgICgMREUFhICIiKAxERASFgYiIoDAQERHg/wEzEy4T\nOSwr8wAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f5cfe5490>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 30000, loss: 0.0790428519249\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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F3UqBxQCFOu4p/tiTvIWaJ3mNouaJHkDXXs6qa//Zkq+c1v6AEokmylqTBMs4\nmgTL18zMh1OmzWTD6u8bzUUy/Zob0KY+2vVMTe/a4PEjB6cTH+Pg3U83k5mVx7/fX8f104cTHRWe\nsXifqSlwQye70aRcRlpr8vPzJDVFB+dTBqVe/3LR9hIGnC4vB7NL2HeohANHSkgYdiNsfxgMC5jH\nnvqVYSM+pQcX3/wIvXt3o3Oy/+YfE9225sHaTc8gr7ACbfpv9DU3eWgbuUZOVFMk24PCZUKVz/+k\nE+jDjmmaPPDza+tdTVSje6++RMfGMv3qGxl82ihsNntAyedy8st566MNlJS5SIiL4Lppw+jSOTbQ\nv1qLWat7CIEEBK01l112ESUlxcyfv0AWF3RESlFhKso8bW+5aH2KSqpYvzWbLTvzyM0vrxW4tNZ4\ny/YTY3ORvWM5Bl6iY6K5ZOZVjDt/Stjm6qCDDxMVFJRjtrOuYw2ljqXNrfAG1gVurObp9KtuwGK1\nMn7iBXw451+8/ve/cNsDjzD96hsbPXdZuYs58zdyKKcMq8Vg2sQMTh/a9Hmc5rIZiuQAA0JhYQGJ\niUmy36CDqVkuWur17yBuy1xuL1t25rE+8wh7Dh7bO2WxKLqkxlKQ9TXduqUz9eJLSE1JaBPfVQkG\n7YBW/jwqZV7d6BxIoLlIsrZtYcH8D/jpXQ8QGRXYD9/j9fHF0p38uOkwAKOGpDNtYkbY5hFs1T0E\nQ+YQTjlaKcrb+HJRU2v2HihiXWY2mVl5uD3+YR+b1WBQvxRGDk6jZ9cEbFYL3y3+kkWfzeO2Xz1C\nercerdxyPwkG7Un1ZFmZx59cq7Ws23KE+Yu34/WZpKXEcN20oSQlRIXl2hFWRZKt8QI5VVVVFBUV\n0qVLw3Mioj1QuJWqXi7a9n6XfabJ/kMlZGblkZmVR2n5sR55zy7xjBySzpD+qUQ4rPi8Xg7u30PP\nPv1bscUNk2DQDunjgkJrraA4klfG3E82U1hSRYTDyhUXDGZg34bzqwdTlE2RaKHByZ+tW7dwyy0/\nYcKEc3nmmefC0iYRfKYyKPVpKj2hKyfZHF6vye4DhWRm5bF1Vz6VVcfSuMTHOhg5OJ0Rg9NIPuEB\naf/uLB6+8xYmXTyDn939P+FudqMkGLRjunoirbyVJtKqnB4+XLCVbbvyAThndE8mjuuNJQyTXrF2\ngzilqW9tV802+lMxLUmHoBSVWlHq0W2mroDL7WXn3kIys3LZsaeg1nr/pIRIhvRLYXD/VLp0jj3p\n2v6qygqb2x4yAAAgAElEQVSyDx2kd/+T1yNoDRIM2jl/bvaaJXbhf4LSWvPd6v0sXL4LraFP90Su\nungIMSFefhqsWgii7VBK4Ua1mQniKqeHbbvyyczKI2tfId7jchylpcQwuF8Kg/ulkJoc3egEsNa6\nTUwSn4wEgw5D4cK/+aY1xlb3HCjiP59vpqLSQ1yMg2suGUqPLnVrUwSToSCxgdTXXq+Xw4cPERMT\nS1JSUkjbIVqm5oHGn2K6dQvNmKZm94FC1m45wtas/KMBQAHd0+MZ3D+FQX1TSEoILJUEQM7hgzz9\n+wd54NGn6NK9Z4ha3nISDDoYUylKvFDZCk9WpeUu/vPZZvYfLsEwFBee04+zRnQL6RORRVFvYrsn\nn3ycFSuW8fTTzzJ48NCQXV+0jFk91FnRynsG8osqWZd5hPWZ2UcngRXQu3siQ/qnMqhvJ2JjAqv7\ncSKtNZ++P4e87CNtcq6ghgSDjkgpSk1FuTv8OzN9PpMF3+1ixdoDAAzNSOWyKQNx2EO3cb2+TWk5\nOdkkJiZht7etHZvC72idAW/rzQs4XV627Mxl7ZYj7D9ccvT1pPhIRg5JY8SgdBLigl/Qqa2SYNBh\nKSq0osTTOmPqm3fkMm/BVtweHylJUVw7bRipyYF/yZrKYVEk2xtfcioC4/V6a5UT9XjcHDp0kF69\n+rTovK29Es7Umr0Hi1m75QiZO3OP5va32ywM6Z/CqCHp9OwanE1gr/z1SQYMPY1zp17S4nOFgwSD\nDkwpqNIGRe7W2aiTV1jBu59sJq+wArvNwmVTBjJsQOeQXS/Kqkiwgqr+emZnH2HNmtV06tSJMWPG\nhuy6HdEvf3kLiYlJ/PrXvyUxMYnMzC3cffcv+eKLr4mIqP20nJeXS3R0NFEn27yoFM7qFUKtMael\ntWbzjlyW/rCX3IKKo6/36ppQvRcgJWi91yVfzCelcxoRkZE8+/9+y5MvvB5Q2pfWJsHgFOBRBoXu\n1nkSc7m9fLxoO5u25wAwdmQ3LpjQD4slNMtPY2wG8YZ/yem33y7ls8/mM2nSVKZOvTAk1+to8vJy\nmTfvfbxeL+vWrSE6OppLLplOVFQ0R44c5sora9cVcblc3HPP7VgsFl588dW6J6zePV8awO75UMkr\nrOCTxduPpoWIjbZz+tAujBycFpLNknP//Q9WLl3I755+geSUzmHNL9QSEgxOET5lUOhpnV9IrTWr\nNhzii2924jM1vbomcM0lQ0OSgVGWnDbNgQP72bhxA5dccilVVVXs2bOL+fPnMX36TJRS/PKXP+Wp\np/7KuHFnA/6f5fvv/4cJE84lLS0dp9PJ/fffyYABg7j33geODq8cn0fI1QpLnsG/OWzZ6n18s2ov\nPp8mOtLGxLF9GDUkHas1+DfoLevX4IiIoN/AIUE/dzg0Jxi0jzAnarFok2QbRFrDv9ZZKcWYEd34\n2VWjiI22s/dQMS+98yMHs0uDfi0NlHpMnFq+poEwDIOnn36C8vJy1qz5kV/96m5GjjyDwYOHMmjQ\nEJYtW3U0EAAUFRXy5Zef8cc/Pk5RURHPPvs0gwcPZfXqVdx//50UFRVVl500yHeZOFspEOw7VMyL\nc1axZOUefD7NqCHp3HPLWZx5WteQBAKAwvxcZj9wOz8ub7yuSEchPYP2TCmKff6lfK2hrNzF3Orl\np1aLwfUzhtOvZ/D3AVgUpDgMMjeuZ9mypUyfPpNu3boH/TrtUWFhIdu2ZTJ27HiUUnz++SecffY5\nxMXFs2DBlwwaNJju3RtOnrZp00b69OnDgQMHmDfvPW6//W4iIhwsXryAqRfPoMQHbrN1NlhVOT0s\n+G4Xq6uTKSYnRjFj0gB6d08My/WdziosFku7rL8tw0SnouqC4WWtsPQUwOsz+XTJdtZsPoLNanDj\nzNPo3S34v6w2Q/HeP/+G1+Ph6quvIz09fCm327K1a1fz5JOzGT36LB566JHgnFQp5rz3H/4z503u\nfOhRho4cHZzzBqhmgvjzpTspr3RjMRQTRvfknDN7hjyr7l9nP0RMbDzX/PR24hPbxwbHE+u0o1T1\nA5SSYHCqUQoqtEFJK600MrVm/qJtrNl8BLvNws2XjwjJjuVIqyLJStusaNRKSktLiI2Nw+v1tPgJ\ntqYIfYlHs37dGkqLiznrnIlUVpRTVJBP1x69gtPokygureKTJTvYsacA8GcLnT55YEiXMh8vc8Na\ntmxYw6VXXU9EZHiy9wbKUNXlfAGb4X9Aqqn4WFOrvab4l8JfGTIpKfD64RIMOoiaX+RCd+ts/DFN\nzYdfZbJhWw4Ou4WfXjGSrmnBr0wWbTNIsOhTOiBkZe0kNTWVlSuX89RTf+DFF//JwIGDW3ROs7rG\nQMUJNQb279nFw3fczJ9eepOExCQ2rP6exOQUhow4vYV/i9p8psn36w6yeMVuPF6TCIeVCyb0ZdTQ\nLk0qBN/eqZobu1K1bvjW6tctaCzK33tq7FfAMBTJyYEHA5mZ6yC0Brs2SbErbEb4f3kMQzHzgkEM\n6Z+Ky+3jjQ/XcySvLOjX+WT+Rzzy6CMcOnwo6OduLx5//H+56KKJeDweXnjh5ZYFAqWowiDPDWX1\n9Cy7du/JuVMvwWq18v23i/l83n/4/tvFBPMZ8lBOKa+8u4Yvv83C4zUZmpHKPTeP4YxhXcMaCMpK\nSxo/KAgU/qd5q6GIsCpibIoEu0FKhEGK3SDVoUizQ7JVE6tMojCxaxOrNlFaY5qNB4JmtUt6Bh2P\nqRTFXqhqhZxGPp/J3M82s21XPlGRNm69alRQu/jz//sWFouVqRdcRK9OiadsD6GlmTObW3by0P69\nPPHru+jVL4OHnvhrs68P/n0ri1fs4fv1B9AaEuIiuHRiBhm9w1NLA6CkqBCA2PgE7rjuUjIGD+Wu\n3zyO3dG83EU1asbxVfX4va365m89OqyjsXCsnnsovsZN7RlIMOiolKLE56+PEG5er8k7n2xk595C\nYqLs3Hr1KDolBn/8NcqqSAigUpqoraEhoUBprSkqzCcpOQWfz4dp+ti0ZhWjzjq78Q9X2747n0+W\nbKekzIVSMG5UdyaO7YPdFt66FcsWfcHzf/w9P73rQc6dcgnLlnzJ1EuvaFKgNRQYSmE1wH7cDd+C\nxqBm+CU0N/yTtkuCgTiq+pe+tBVWGnm8Pt7+aCO7DxQRF+Pg1qtGNSlVcKAcFkWS7dSppZybm0NZ\nWRldu3ark0qiUdVpJEqCkEto3aoVvPnSs5x/4aUc2LubH5Yt4f/e+ICk5JSTfq6s3MVnS3eyZWcu\nAF1SY5kxeSBdOse2qD1N5fP5uP3qi+nasxf3PvIHfF4vnTqnBfRZQ/nH8h0Whf2EG39bup1KMBC1\nKAWV2qC4FVYauT0+3vxwPfsOl5AQF8GtV41qceZIn9fL2/98nt3bt/L7v7zkXwduKJLsCmsHDgjf\nfLOE5cu/wzAUK1cuZ+rUi7jzznsD/rxPBbdo0vYtGyktLmLUWWeTe+QQaV27n/Rp2tSa1RsPs3D5\nLpwuL3abhUnjejNmRLewVNM7kdaanCOH2L87izPPPq/R443qYZ4oi8JhgA3dpm789ZFgIOrlVq2z\n0sjp8vLGh+s5mF1KYrw/IMTHtiwgvP/Wq/TqN4CRo8diqc7GaVGQYDeIVB0zdcWBA/tZsmQh3bv3\nZOLEyYF/sLrGQFkr1hjIyS9n/qLt7D/in6DN6J3MpRMzSIgLfk8xUPt3Z/HlR//l1nsfarCkqqI6\nAFgVEe0kABxPgoFoUGvlNKpyenjjw/UcyikjKT6SW68eRVwzi4ucjAJi7Aaxhj6a7fRUpg1FiTc8\nO9QrK8o5tH8P/QcNO/qa2+Nj6fd7WLH2AD5TExNl5+Lz+jM0I7VVy0bm5RzhiV/fxYTJFzHj2pvq\n7M+wGopIqyKyOgC016cLCQbipFqrelqV08PrH6zncG4ZyQmR/Oyq0AQEgAirIsFau0BOe+V2u/nd\n7x5i2LDTuOGGmwO+iYYz8LtdLn5+xRSuvuV2LrrsagyLhfVbDrD4+wP+CWLgjGFdmHJ2XyIjbCFv\nz8lUlJfxwh8fZeb1PyVj8LHAZTEUkRaItCjsaFQrTPgGm+wzECdlaE2i1Z8eOpzPZpERNm6+YgRp\nKTEUFFfxr/fXUVZdkrCpCvJyeOqRX/HEr++q932nV5Pn1jir92W2Z1przj13IpWVFQEFAqXAiUGe\nywxbD9DucDB1+pWgNb+586dMO2sQj94+g6KiMtJTY/jFtaczffLAVg0EWmuqKisoKSqksCCXPTu3\nYTEg2qro5DDobIcEi8auTQhgQ1dHJD2DU5aiEhX2FBaVVR7+/cE6svPKSU2O5udXj2ryTcJZVcmK\nrxfSZ8AgevXNaPA4hX/HcpxVnxLLT3V1nqrWKJHq9vhYunInr//1t7irSjlt2sNMnTCA0cO7YrTC\nJsgTvfj041RUlPGbx/+Mw6L8PQClsXSAHkBDZJhINIlHGRS5w1uxqqLKzWv/XUteYSW9uyVw08wR\nIUtFDP5lgIl2hZ32NblcWFjABx/8l1/8Ylajx5rKoLh6tVA4aa3ZtD2HBd/toqTMhddVwchhPTmt\nj4NF898lMbkTP/l5/T24cCjIyyExKQlnWQnvvPp37r/vQeJjotvV96C5JBiIJjOVotQHlZ7w5asv\nLq3ilblrKKtwM2xAKldeNKRZqQdM0wyo+pShINZmEN2OJpdXrPiOp556gr/+9QX69u1X7zE1OamK\nWqH63cHsUr5YuvPoKqG0lBguOa8/vbolsn93Fj+u+IazzplITFwCpUUF7N2dxaJP5+F2VmGPiGTK\ntJmMO39qyKqHWQ3FS0/PZtGXn/D8c/9g5Mjg5lNq6yQYiOapXoJY2sxdqc1xJLeM195bi8vtY/zp\nPbjwnPpvePXZtnkD//y/P9KzT3/u+e3/C/hzDosi0dZ+JpedTieFhQV06dK1nncVFTq8PzOA0nIX\ni5bvYl1mNgDRUTYmj+vLqCHpdYaEdu/Yxu/v+zlKGZSVluBxH5snstkd9O4/gEefealZdYV9Ph8r\nli6sFWCmXjqTSZMvIMZmwaH8K4EKCvKJiooiso1lIQ01CQaiRcI9bJS1r5C3PtqAaWouPq8/Y0cG\nVrQmPyebA3t3MXTkaGz2pqVuthzXS2i34wXV6UYqPOGbH/B4faxYe4BvV+3D7fFhMRRjR3bn3DG9\niHDUX4C+oryMX992A3uztjd43owhw/nLq3Ob1EMoLixg9oOz2LNze60AY7c7GDBgAMOHj2T37ix+\n//v/d8rWvmhqMKj/JyhOWTZt0smuKPUpKjyhv83065nEzCkD+eCrrXyxdCdxMQ6G9E9t9HOdOqcF\nnD7gRD4NxW4Tt1URZzXaZC/hpZeep3PnNC688GKiomon+vNVzw84veFr9679hXy0cBvFpU4ABvbt\nxIXn9CO5kSL0635YzqH9e096zJ6d21m5dBHjJ04NqC2maTL7wVns2LKxzntut4tNmzbi8XgZNuw0\nkpPDl/SuvZOlpaIOQ2sSLP4dveFYCDJicDqTx/dBA+9/kcneg8VN+nxzO7eV1UtQqzCOlYpqI9LT\nu7BmzY8n9IZr0k03LdNoS3i9Jl9+m8XrH6ynuNRJanI0t1wxguunD280EAAs/HRerSf3+njcLhZ+\n8kHAbVr59QL27Gy4pwGwe3cWPXv2wt7EXuOpTIKBqJ/WxBgmnRxGWOojnDO6J2cO74rXZ/LO/I3k\nFlQ0+pkvP/ov1184nrdffq7Z1/WZmiKXSYEXvMpoMzHhssuu4A9/eJqYGH8331SKYhOKXGbYUork\nFVbwyn9Ws3zNfgylmDi2N3fcMJq+PQIvB+l2VgV0nMvlDOg4m6FY+nnjAcbtdvPDDysCOqfwk2Ei\n0SCtwUZ4ho2UUlxyfgalFS627crnrY828MtrTif2JLuUzzpnEqPHn0tiI5kyG6Pxb1Rz+zQx1XMJ\nRivNJZSVlWGxGEeHhlR1ptHiMK4W0lqzetNhvvhmJx6vSWJcBFdeNKRZpUztEYHlH3I4Tp6vSimI\nthrEWnTAAaaqKrAAI/ykZyAaFa5hI8NQXHXRELqnx1Fc6uTNjzbgdHkbPD4hKZnklM5BW5poaih1\nm+S5abWho2XLljJp0gReeeVFtKEo9ikKXGbYAkFFlZt3PtnE/MXb8XhNRgxK444bzmx2Tesp02Zi\ns5887YjN7mDKpVc0/L7h3yWcYDExtCYiwAATGdmyhIinGgkGIjDVw0bJDgNrCCOC3Wbh+hnDSU6I\nJDuvnLmfbsLrO/lEqdfrCWobvKam0GWS7/Fnew1nULj44ktZunQl06+8jjwXlIdxtVDWvkJeeHMV\n23blE+GwctXFQ7jiwsENrhQKxLjzp9K7/4CTHtO7/wDGnlc3E6uhINZukOLwl3St6azNmDETeyMB\nxm53MGNGwwFG1CXBQATs+DrLkdbQ3SCjI+3cNHME0VE2du0v4uOF2+qdJNZac9vVF3HFeaNwVlUG\nvR0unybf6Z9PcCsj5Jk2lVJ4lEGVLQIzJjFsy3u9XpMvvtnJGx+up7zSTc8u8dx5w2iGD+jc4nMb\nhsGjz7xExpDhdXoIhmGhc5duPPrMS0d7d1prjhw6gM2AZIdBvGHWSSUyadJUunc/+RLkjIwBTUv1\nLWSfgWim6jw4ZZ7QpXg4lFPKv95bh9vj49wzezJ5fN86x+RmHyapUwpWa2iToCnAYVXEWv1ZLYP1\nlzZNk4WLF/Dxx/PYsWMbndO7Mv2am0K6M/d4uQUVvPfFFrLzyjGU4vyxvThndK+g5xMyTZOVXy9k\n4acf4nI5/XUolOKCaZczYcrFuJxOPpr7OpiaOa/9neeff5lxY8cf/XxpaSm5udn06+fPRXX55dPw\neNzk5OTgPmGfQUbGAJ577iWSmrGRrSORTWcibJQCpzYo8oSuaM6OPQXM+XgjptbMmDyQM4a17gYi\nBdgsimirIqIZic6UAhOFD0V2QQEP3nMbu3bU3jhls9npnTGw2TtzA6G15seNh/jimyy8PpPE+Ijq\n+ZrmzQ201BO/vguF5sbrb2L5t0v4yU9uqrXrOitrB7fd9jPuv/9/mDZtBu+++xZnnTWOrKws5s//\nkKoqJ5GREcyYcQUTJ04OSyBt6yQYiLDzKX9AcIUoZfLqTYf4eNF2DKW44bLh9O9V+wZpmiZVlRVE\nx4S3jq5F+dNbRFgUtuo6uAr/WPfxv1U+wIvCY4LL1LhN8Hp9/Orn19a7capGc3bmBqKi0s28hdvY\nvjsfgJGD07jk/Awc9tZZXGgxFFSWkJYQf9Ie17ZtW3E4HPTu3SeMrWu/pJ6BCDuLNkm2+4vKhMIZ\nw7pyzuiemFoz99PNtTalrV7xLVeefzr//L8/heTaJ+PT/o1rhS6TPJdJjhty3HDEBbkeyPP4/3+u\nyz/3UOw2qfL6e1HLA9g4VbMzN5iy9hXwwlur2L7bP0l89cVDuPyCwa0SCJTy19VItUNafNzRQLBv\n317+8Y8XKC31J8BbvnwZZWVlDBw4SAJBCEkwEEGhTE2SLXQBYdL4Ppw2KA23x8eb89aze38hAENH\njebtz5Zx3+/+EJLrBsrU/g1s3up/3D5/T8ljanyaOiuCQrEz92S8XpPPl+7kjQ83+CeJu8Zz5w1n\nMiwIk8TNYbfULBetu6dj/vx5vPzy39m8eSMrVy7nzTf/zYED+1qlnacS2XQmgkaZmkSrolCroA8Z\nGUpx+dRBGArWZWbz1kcbuXbaUAb0aZ+5Z4K9M/dkcgsq+O/nW8jJr5kk7s05o3u2StEZo7o3EGto\n0PUvm501626uvfZ6UlJSyc3NYdCgwdhsrVsu81QgwUAElaE1STaDAgh62UXDUFw2dRAWi8HqTYeZ\nM38j087P4PQhaezJ2k5BXg5jJkwM6jVDJVg7cxuzZWcuH3yZicdrkhQfyZUXDW61SWKHRRFva7zI\nkNVqJSXFn6wwNbUz9933YJhaeGqTYCCCztAmyTaDfE3Q18obSjF90gBiouws/WEvnyzZweEjuSx4\n81EGDh3RboLBlGkz2bD6+5MOFTW2M/dktNZ8++M+Fi3fDcDwgZ2ZPmlAq8wNWKp7A/7CQuEvySkC\nI6uJRMj4lEFBCGsjrN1yhI8XbcM0NYP6pXDlhYOx2ywhuVawmabJAyFaTeT1mny8aBvrt2ajgMln\n92XCGT1CvmmuPhFWRYJVYW1nJUc7AllaKtoUrzIoDGFA2L2/kHc/3YzT5SUtJYarLx5CSlJ04x9s\nA2oKtOzalonPdywHU0sqgFVU+nML7T9cgs1qcOVFQxjcr2WJ/JrDYijibIoo1Y4LCLVzEgxEmxPq\nHkJuQQX/nvsdB3dnEhEVy3XXXsLIwWmt8iTcVKZp8t2Sr1jy2Ue4XE4cjgimXHoFY89r+sapnPxy\n3v54I8WlTuJiHFw/YzhdUsO790IBUTZFnEVhtMGiQacSqXQm2hz/PgSDQk/wJ5UBUpOjOWsAzFmx\nCrPTacxbsJWsfYVMnzSgRUnWQm3pV59QVVnJmWefxzmTL2rRubL2FTD308243D66pcXxk0uHnTT9\ndyjYDP8EsQP/SiHRvkjPQISNqQwKPDokAQH8k6brM7P59OsduD0+EuIimDllIH2aUIwlnJYt+oIf\nV3zDtCuvJ2PwsGafZ/WmQ3yyeAem1gzpn8oVFw7CZg3f3EnNctEYi66TVE60HhkmEm2aqQwKQ5i6\nAiC/qJL3Pt/C4dwyAM4c3pWpE/q2WrqFUDG1ZtHy3Sz70b8ha8Lonkwe3wcjjMNjEVZFvFVhkwni\nNkeCgWjzTKUo9BD0gLAjcxPbNq/nzLPPJ6VzF5at3sfS7/fiMzUJcRFcNnkgfXu2zV5CU3m8Pj78\naiubd+RiKMWlkzI4Y1jXxj8YJDJB3PZJbiLR5vk3pvk3IQXTj8uXsn93Fh63G4vF4Lwxvbn9+tF0\nSY2luNTJ6x+u5+OF205aPS1cNqz+njdeepatm9Y1+bMVlW7+/f46Nu/IxWG3cOPM4WELBAqItilS\n7YooTAkEHYj0DESrMZVBfghXGdXw+Uy+W7Ofr7/fg8+niY91MGPywDrZT8Npb9Z2vlvyFT379GdC\nEyaPD+WUMvfTzRSXOomPdXDDZaeR1inwp7+WsNfsINaautmWRFsjw0SiXfFVB4Rw1PjNyS9n3oKt\nHMrxzyWMHJzGhef0JyqyfeS9WbP5MJ8u2YHXZ9K1cyw/mT6cuDCsGFL4y0/68wnJ72B7IcFAtDte\nZZDvNmmk1HFA1n7/HSu/WcRl191M1x6967zvM01WrDnAkpV78PpMoiNtXHRef4YP6By2fQl/euR+\n4uITueG2u4mLT2z0eI/Xx+df72T15sMAjB7WhYvPy8BqDf0or6EgwW4QpWSCuL2RfQai3bFqkyS7\nQaHLpKVzyocP7CM1vWuders1LIbBhNE9GdQvhfmLtrHnYDHvf5HJui1HuOCcfqSnhH6T1oxrb2Lb\npvVEREQ1emxxaRVzP93MoZwyrBaDSydlMGpIeKq9WQ1Fkl1h0xIITgXSMxBthguDQrdJuH7MWmvW\nbjnCV99mUeXyooCRQ9KZNK5PWIZfGpO1r5D3Pt9CpdNDQlwE100bRpfO4dlRXJNTyCKbx9otGSYS\n7ZZSUKkNitzhfRKtrPKw9Ic9/LDhEKapsVkNxp/eg7PP6BH0vQla60aHo0ytWfbjPhav2I3W0L9X\nEldeNISoiPDMbUTbDOItGtU+bg2iARIMRLumFJSbBiXu5qU6dlZV8uGcf1FUkM+dDz3WpM8WFFWy\n4LtdZGblARATZWfSuD6MHJKGJUh1iH9398+wOyK4/YFHSE2vuxy0rMLFh1/502kAnH9WL84b0zss\nhWgMBbE2gxiZKO4QJBiIDkBRrhUl7qYPUfi8Xua8+gI9evfj3KmXNGtSeO/BYr78dufRVUfJCZGc\ne2Yvhg/q3OKgUFZSzOqVyzjrnIlERh3Lrupye1m57iDL1+zH6fISFWHj8gsGha2Sm8WARJtBhEwU\ndxgSDETHoBSlpqKsGQEhGEyt2bwjl0XLd1FU4i89mRQfybljenLawDQsluD0FKqcHtZlHuHbVfuo\nqPIA/mGhy6YMCtu8hcOiSLAprDI/0KFIMBAdh1IU+xQVnta7SflMk41bc1i6ai+Fxf66xYlxEYwd\n2Z0Rg9OIbMI4vmmaGIZBWYWL3QeKyNyZx/Y9+fiql1B1S4tjyvg+YU2sF21TxFuRBHMdkAQD0bEo\nRZEXKr2B/+z379nFR+++TmJyCjfedk9QmuEzTTZtz+WbH/aSX1QJgNViMLh/Cv16JNGnRyLxsfXX\nK3a5vew9WMzfZt9HfvYhup15E9FJPQH/HEmf7omMGdGNgX06hW2vg1IQJ/MDHZoEA9HhaENR4A48\nsd2RQwdYs+JbBp92On0yBga1Laap2bY7n1UbDrJrf1Gt9xx2C3ExEUQ4LDjsVqxWg6KSKvIKKjG1\nxvR5cZZlEx2XQt/e6fTvlcTQjM5hX8Zqqd5IFinzAx2aBAPRIYUrj1FTFBZXsm13Abv3F7L3UDEu\nt6/e4wyl6JoWS9/qHkT3tPiw7B6uj616I5nMD3R8EgxEh+VTBnluja8J34OacfpQ01pT5fRSWuHC\n5fLicvuOFthJTY5m/Q/fMmzUmbVWEIVbpFWRYPVnjRUdnwQD0aF5lEFBAHmMnFWV/GbWTeTn5vDW\nZ9+2aj1kn8/HY/f/ksMH9/P3OR8TEdl4Gopg8qedNoiTjWSnFAkGosMLNCBs27SeXv0ywn7zbYjH\n7cZmt4f1mgqItxtEK0k7faqRYCBOCV5lUBCm1NftlaFqAoFMFJ+KpNKZOCVYtUknu8LeSLU0rTWV\nFeVhalVdpmny8dw3yTl8MKzXNRQkSiAQTSDBQLRbFm2SbPNPjNZn26b1XH/ReJ559NdhbtkxzqpK\nDuzdxR9+cw/h6oRbFCQ7DCKkSL1oAhkmEu2fUpRU71Q+/hvidFZRWVFOYlL4NnM1JJBspcFgMRTJ\n1S99KeMAAAo3SURBVDUIxKlNituIU4/WxBtgcxiUuo8VyImIiCQiIrJ121YtHIHAVh0IpAaBaA4Z\nJhIdhCYKk04Oo848gsvpxOmsCnuL3n/rVZ578n/JzT4c8mvZLRIIRMtIMBAdilWbdLJBjM1AKXj5\nL3/g2qljWLPi27C3ZeSY8fTql0FRQX5Ir+OwKJJtEghEy8icgeiQlPKX0TxYUILVEYnF2jFHRCOt\nikSbZB0VdcmcgRD4E3HaMemdHEe5qSj3hK+2crhEVaeXkEAggkGGiUSHprQmVvnIy9rC9g0/hu26\nhQV5PP7gHbz72oshOX+0TZFoRdJLiKCRYCA6vG+++ZqH/+deyrIPkugwsIShnnBkZBSTLrmMlLT0\noJ87xmYQb0HqEIigkjkD0eH5fD6UUkezl5pKUeZTVHjb16YspSDeZhAtBWlEACQdhRAnsFgstdJY\nG1qTYNH1LkMNhtKSIlxOZ1DPaVGQZDeIMUwJBCIkJBiIU0Jubg6ff/4JK1cuB/w7gu3aJMXmT+YW\npPr2ACxb9CU3X3ou3y78PCjnsxpK0kuIkJPVROKUsGPHdpYsWcSUKRfUfkNrYpQmym5QbkJFEFYd\nXXLFdZx59nktO0k1h0WRKHsIRBjInIEQ1ZQCDwblPk2lV7f6U3iUVZEgewhEM8mcgRDNpLV/B3OC\nAZ0cBhFWRVNnFPbs3E5hfm6L2qGAWLvhXzoqgUCEiQQDccpYt24N//73P9m3b28jR/rnE5Kt0CnC\nwNGESebvFn/JrOsuZd2qFc1qo8VQJDoM4pSsGBLhJcNE4pTx2msvs379WiorK1FKERERyYwZM5k0\naWqt1UZ1KIVTK8q8Grev8e+gz+sFaFIKDKUg2moQa9FSsF4EhZS9FKIehYUF3HPPLHbs2I7b7Tr6\nut3uICNjAM899xJJScknPYeuCQoejSdI30Wl/JPEsVaFQ1YLiSCSYCDECUzT5KabrmXz5o0NHjN0\n6HDefHPuyXsI1bRSuLSi3Ktxm8cmmld9t5S4+AT6Dxp60l6Bwj8cFGlVRBlgQ4etCpo4dcgEshAn\nWLx4ATt2bD/pMTVLTwOhtCYC/x6FVIdBvN0/r+CsKOOJX9/Fnqza1/Lf/CHCqkiwG6REGKTaId4w\nsWpTAoFoE6RnIDq8u+66je+++6bR4yZMOJfnn3+5WddQSuEDKqpcOCIjMDXU7AywKrCi8acTku+w\nCA9JYS3ECQKtclZV1fwUElprDCA2wg4nbhDTtf4Qok2SYSLR4QVaBzkyMqJZ59+2LZN7753FwoVf\nNuvzQrQFIekZ7N27l7fffptVq1Zx4MABoqOjGTZsGPfeey8DBw4MxSWFaNCMGTP/f3t3E9pEGsYB\n/N8GOxYlie7BJKSiNFIb8YOACpWFkoLCHrSloqgHVwvVYkTbUKR+YA1s8KIVUxFBsBRCU8E1RlSk\nVC+7bdOukUJpBeNFW9Ie1DSmpn6E2cOu7sZkkzZmOsn2/zs+M+/kOQx5mPd9Zx709/fF7CL6VkGB\ngB07qtO6vl6/HNu2/YSpqal0UySSnSRrBk6nEzdv3kRVVRWMRiNCoRCuX7+O4eFhuFwuGI3GWV+T\nawaUrkzvJiLKBVmxtTQYDEKtVsfEwuEwzGYzzGYzzp8/P+trshjQ98jEewaJhMNhFBYWQqFQZDJd\nou+WFQvI3xYCAFi8eDFWrFiBiYkJKX6SKKmlS39Ae7sL3d1d8Hh+RSQyDYUiH2q1GiUlxrQKAQB0\ndjpx964bzc2/YMMGU4azJpo7c7a1dHJyEuXl5aiursbp06dnPZ5PBpRpz56N4NatTmi1Ovh8TzA9\nHZn5Jyr+Jooient/R1HRchQVLZ+DrIlmJiumiRKxWq149OgRPB4PioqKZj2exYAyTaqpI6JsIEkx\n6O3txYEDB1JebNOmTWhvb4+LX7t2DZcuXYLdbkdVVdWMk/s3FgPKpO9dVK6t/RlarQ719Y1Qq5dI\nmSpRWiRZMzCZTHjw4EHK8woL4/dzd3R0oKWlBQ0NDSkLQSgUQigUiokpFApotVrk52e+Vy3NXz09\nv2FqKgy9Xv+f50xNheH19mDLlh/jjtlsdjx58geUSiXvTcpKX+7LQCCAaDQac0ypVEKpVMbEJJ0m\ncrvdaGpqwsGDB9HY2JjyfIfDgdbW1piYyWRCR0eHVCkSEf2v7dmzBz6fLyZmsVhw9OjRmJhkxaCr\nqwvHjx/Hzp07ce7cuRmNSfRkMD4+jgsXLuDixYvQarVSpEqUlkAggH379sHpdPLepKwTCATQ0NAA\nq9UKjUYTcyzRk4EkW0sHBgZgtVpRUlKCyspKDA4Ofj1WUFCA0tLShOMSJQgAPp8v7jGHSG7RaBRj\nY2O8NykrRaNR+Hw+aDSapNOhX0hSDLxeLz59+oSRkRHs3bs35phOp0N3d7cUP0tERGmSpBhYLBZY\nLBYpLk1ERBLgh1iIiAiK5ubmZrmTSEUQBGzevBmCIMidClEM3puUzWZzf+ZMpzMiIpIOp4mIiIjF\ngIiIcqwHMjuoUTYYHx+H3W5HT08PRFFEWVkZTp48yRfPSHYPHz7EvXv3MDQ0hNevX0Or1WLr1q04\ndOgQFi1alHRsTq0ZSNFBjWg2pqensX37dgiCgPr6egBAS0sLPnz4AI/Hg4UL0+ujTJQJu3fvhk6n\nQ0VFBTQaDYaHh+FwOFBcXAyXy5V8sJhD3r59Gxd79+6duHHjRvHEiRMyZETzTVtbm2g0GsWXL19+\njb169Uo0Go3ijRs35EuMSBTFN2/exMVu374trl69Wuzr60s6NqfWDNhBjeT2+PFjrF+/PqYnh16v\nh8lk4pv1JLslS+I/p7527VqIopjyPzKnikEik5OTeP78OYqLi+VOheYBv9+PVatWxcUNBgNevHgh\nQ0ZEyfX39yMvLy/lf2TOFwObzQYA2L9/v8yZ0HwQDAahUqni4iqVKu6Lu0Rym5iYgMPhQFlZGdas\nWZP0XFl3E2Wig9r9+/dht9vTaqVJlI68vPhmNmLu7MOgeeL9+/eoq6vDggULYLfbU54vazGYqw5q\nRJmiUqkQDAbj4qFQKOHn14nk8PHjRxw+fBhjY2NwOp1YtmxZyjGyFgNBELBy5cpZj3O73bDZbKip\nqUFtba0EmRElZjAY4Pf74+J+v5/rVpQVPn/+DIvFgqGhIbS1tcFgMMxoXM6tGXR1deHUqVPYtWvX\njFppEmWS2WzG4OAgRkdHv8ZGR0fx9OlTVFRUyJgZ0V/TlVarFV6vF1evXsW6detmPDanXjobGBhA\nTU0NDAYDzpw5g/z8f2pZsg5qRJkSiURQWVkJQRBw7NgxAMDly5cRiURw586dhFOaRHPl7Nmz6Ozs\nRF1dHcrLy2OOaTSapNNFOVUMWltbceXKlYTH2EGN5kqiz1E0NTVBp9PJnRrNc2azGYFAIOGxI0eO\nJG06llPFgIiIpJFzawZERJR5LAZERMRiQERELAZERAQWAyIiAosBERGBxYCIiMBiQEREYDEgIiIA\nfwJjXXWGtExIEgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f5b87ee50>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 40000, loss: 0.438342481852\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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TcoTxiWbHIt5u4HbYai9qWqJmsZ2zhmaR1bkDPn+IooNV7NryFZvXrWDDnhB/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\nTG3K0eAAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f5b8dee50>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 50000, loss: 0.274243146181\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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qqKisb/e2bBgwKCGKpIRobDaD+FgXCXFuEuLcxAd/JsS6iYlxYm9xgwu1BezavhVfU+eB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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f5b68e3d0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 60000, loss: 0.0882532298565\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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RW0czdvykZvcd1LU3e3vY5g98GorcGkuqpwnRaUXMb/ea7/4TcCK3ziCQfQd1eTxuFsz9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\nqJlHsEd4sjtLGZT5NJWe1i8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            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f5c776810>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 70000, loss: -0.293868511915\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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H3jBdxLTpSOfzf0pMQse69vvQ6+7Etuo/UDXwxLWlR+5E3DHBzV22bbEx73eU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\nVQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f58e26f50>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 80000, loss: -0.406084805727\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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oDHUnnbW3ve6mMijw6UZ3qHrwjh9z6GAmf5n+3yZtTQP/z/b+n99Q711MxpDh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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f58d9ed90>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 90000, loss: 1.34461963177\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Nkt2k7srFbDJw/ZSh9EwObIz92tRD/LRqHwKYetEARgwMbKizQUCMRcGkqVRU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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f577b5d90>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "pudKobiUJbbT",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### ANP training\n",
        "\n",
        "Next, we train the ANP with multihead attention, using the same hyperparameter setting as NPs. Note that the predictions are now much more accurate for the observed context data."
      ]
    },
    {
      "metadata": {
        "id": "q6wQwAwjTEc_",
        "colab_type": "code",
        "outputId": "79adcd77-3af4-41ca-d01c-7ded9ef6fa4e",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1548700486631,
          "user_tz": 0,
          "elapsed": 2728390,
          "user": {
            "displayName": "Hyunjik Kim",
            "photoUrl": "https://lh5.googleusercontent.com/-oMZCZLTka34/AAAAAAAAAAI/AAAAAAAAAAc/ENlUKunKSqo/s64/photo.jpg",
            "userId": "01465310974685628261"
          }
        },
        "colab": {
          "height": 2897
        }
      },
      "cell_type": "code",
      "source": [
        "TRAINING_ITERATIONS = 100000 #@param {type:\"number\"}\n",
        "MAX_CONTEXT_POINTS = 50 #@param {type:\"number\"}\n",
        "PLOT_AFTER = 10000 #@param {type:\"number\"}\n",
        "HIDDEN_SIZE = 128 #@param {type:\"number\"}\n",
        "MODEL_TYPE = 'ANP' #@param ['NP','ANP']\n",
        "ATTENTION_TYPE = 'multihead' #@param ['uniform','laplace','dot_product','multihead']\n",
        "random_kernel_parameters=True #@param {type:\"boolean\"}\n",
        "\n",
        "tf.reset_default_graph()\n",
        "# Train dataset\n",
        "dataset_train = GPCurvesReader(\n",
        "    batch_size=16, max_num_context=MAX_CONTEXT_POINTS)\n",
        "data_train = dataset_train.generate_curves()\n",
        "\n",
        "# Test dataset\n",
        "dataset_test = GPCurvesReader(\n",
        "    batch_size=1, max_num_context=MAX_CONTEXT_POINTS, testing=True)\n",
        "data_test = dataset_test.generate_curves()\n",
        "\n",
        "\n",
        "# Sizes of the layers of the MLPs for the encoders and decoder\n",
        "# The final output layer of the decoder outputs two values, one for the mean and\n",
        "# one for the variance of the prediction at the target location\n",
        "latent_encoder_output_sizes = [HIDDEN_SIZE]*4\n",
        "num_latents = HIDDEN_SIZE\n",
        "deterministic_encoder_output_sizes= [HIDDEN_SIZE]*4\n",
        "decoder_output_sizes = [HIDDEN_SIZE]*2 + [2]\n",
        "use_deterministic_path = True\n",
        "\n",
        "# ANP with multihead attention\n",
        "if MODEL_TYPE == 'ANP':\n",
        "  attention = Attention(rep='mlp', output_sizes=[HIDDEN_SIZE]*2, \n",
        "                        att_type='multihead')\n",
        "# NP - equivalent to uniform attention\n",
        "elif MODEL_TYPE == 'NP':\n",
        "  attention = Attention(rep='identity', output_sizes=None, att_type='uniform')\n",
        "else:\n",
        "  raise NameError(\"MODEL_TYPE not among ['ANP,'NP']\")\n",
        "\n",
        "# Define the model\n",
        "model = LatentModel(latent_encoder_output_sizes, num_latents,\n",
        "                    decoder_output_sizes, use_deterministic_path, \n",
        "                    deterministic_encoder_output_sizes, attention)\n",
        "\n",
        "# Define the loss\n",
        "_, _, log_prob, _, loss = model(data_train.query, data_train.num_total_points,\n",
        "                                 data_train.target_y)\n",
        "\n",
        "# Get the predicted mean and variance at the target points for the testing set\n",
        "mu, sigma, _, _, _ = model(data_test.query, data_test.num_total_points)\n",
        "\n",
        "# Set up the optimizer and train step\n",
        "optimizer = tf.train.AdamOptimizer(1e-4)\n",
        "train_step = optimizer.minimize(loss)\n",
        "init = tf.initialize_all_variables()\n",
        "\n",
        "# Train and plot\n",
        "with tf.train.MonitoredSession() as sess:\n",
        "  sess.run(init)\n",
        "\n",
        "  for it in range(TRAINING_ITERATIONS):\n",
        "    sess.run([train_step])\n",
        "\n",
        "    # Plot the predictions in `PLOT_AFTER` intervals\n",
        "    if it % PLOT_AFTER == 0:\n",
        "      loss_value, pred_y, std_y, target_y, whole_query = sess.run(\n",
        "          [loss, mu, sigma, data_test.target_y, \n",
        "           data_test.query])\n",
        "\n",
        "      (context_x, context_y), target_x = whole_query\n",
        "      print('Iteration: {}, loss: {}'.format(it, loss_value))\n",
        "\n",
        "      # Plot the prediction and the context\n",
        "      plot_functions(target_x, target_y, context_x, context_y, pred_y, std_y)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration: 0, loss: 1.42949461937\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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kpPYyh0FBQdi3b1+9r/v+F98gNzsTTZt7NyQ8Qdhqo1ptooaPxp2b1+Hk5CLI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\nkpXOCgoK4OnpqbGtuLgYERERiIiIwNK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            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f55529190>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 10000, loss: 1.30306947231\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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7XG/OH9+vxfUNCYld2bRuFQrFU396i8SuSeTn5vDD92tZvXI5675dybpvVzJizKm8+acX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\nGlcM4y1RAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f5bc3e0d0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 20000, loss: 0.436478257179\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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nn2Xu3F8yePDQ6u35+XnMmzeb9PS0Oi/tr77aytKlr7K4mQSDqgQMHYFXmkkD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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f4d040090>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 30000, loss: -0.564530730247\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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wSbBbuOPesbz90Vo2bStg0fIdXDW0J25t4IrgbKd9+/YRDNZ8aExKSiIpKanG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\nrkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f4d16b2d0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 40000, loss: -1.08188056946\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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RFHhD0dXgSgSOCmEAMHr0GM4882wGDcrv76nEBSFExAgCEYVjtVG3zC/hHL3d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\nMBBCCIEEAyGEEEgwEEIIgQQDIYQQwP8DS4kvbNkpAvcAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f4de86f10>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 50000, loss: 0.485689043999\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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efXI8rVYZ3PvI46AzcvYlVxIRGVyz9dCBfcx9+lEGDB3BVTfdidXmJK+gnIzs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\nAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f56b880d0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 60000, loss: 0.134729295969\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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OxpBhjI+Q112I46EU5OZXBoPoulZGjjmZ5e+/yV8ff47tWzbw0TuvE/J7rc1nps1g4sRJ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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f4e5da1d0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 70000, loss: -1.29039406776\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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dGhZ8OQeg2i6itm3z+dfrsG04/aTjaFTSny/+92F5fW9VXG4P/QcNLf9/t8tB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\ngsJARERQGIiICAoDEREB/h+J1fsxO/nHGAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f4dca71d0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 80000, loss: -0.624202787876\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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tErEU9U2tuyE89thDnHnmXHbu2olK8cYSAoJCUhmCSr9FXdDCF1aE2yz6yfBF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\n69l8vhMAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f4dcd2e50>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Iteration: 90000, loss: -1.33056414127\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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GgsmT/8mNN17L0aNHGu2aLSYYJHeN4ci+n/l1764699u1K40VK5Y1UqmE8I1S3vHuulK4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\nR5BFw4YEAiFEyyLBANi0aSNjxtzN669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            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8f4c9dbe90>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}
